Question

AXYZ has vertices X(-4,2), Y(4.2), and Z(0, - 1). Is AXYZ scalene, isosceles, or equilateral?

Is AXYZ scalene, isosceles, or equilateral?

Answer 1

Isosceles triangle.

Explanation:

In order to determine the nature of the triangle, we will need to get the sides XY, XZ and YZ using the distance formula;

For XY;

X(-4,2), Y(4.2)

XY = √(2-2)²(4-(-4)²)

XY = √(4+4)²

XY = √8²

XY = 8

For XZ;

X(-4,2), Z(0, - 1)

XZ = √(-1-2)²(0-(-4))²

XZ = √(-3)²+4²

XZ = √9+16

XZ = √25

XZ = 5

For XZ;

Y(4.2), Z(0, - 1)

YZ = √(-1-2)²(0-(4))²

YZ = √(-3)²+(-4)²

YZ = √9+16

YZ = √25

YZ = 5

Since XZ = YZ = 5, this shows that two sides are equal. Hence the triangle is an isosceles triangle.

NB: Isosceles triangle only have two of its sides and angles equal